We employ first-principles methods to study the topological properties of stanene and stanene-like materials by scaling stanene's natural intrinsic (atomic) spin-orbit-coupling (SOC) strength from 0 to 600%. Quantum phase transitions are observed in this two-dimensional system involving two different gaps. Stanene with zero SOC is a Dirac semimetal with a Dirac cone located at . An infinitesimal SOC opens up a gap at and the system becomes a two-dimensional topological insulator. Increasing the SOC to 333.3% causes the system to become a Dirac semimetal again with a Dirac cone located at . Further increasing the SOC causes a gap opening at , and the system becomes topologically trivial. This behavior is contrasted with that exhibited by three-dimensional topological insulators such as Bi2Se3, for which a strong SOC is a necessary but not a sufficient condition for the formation of topological phases. The similarities and differences are discussed.

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